List of things named after James Joseph Sylvester

The mathematician J. J. Sylvester was known for his ability to coin new names and new notation for mathematical objects,[1] not based on his own name. Nevertheless, many objects and results in mathematics have come to be named after him:[2]

• The Sylvester–Gallai theorem, on the existence of a line with only two of n given points.[3]
  • Sylvester–Gallai configuration, a set of points and lines without any two-point lines.
  • Sylvester matroid, a matroid without any two-point lines.[4]
• Sylvester's determinant identity.
• Sylvester's matrix theorem, a.k.a. Sylvester's formula, for a matrix function in terms of eigenvalues.
• Sylvester's theorem on the product of k consecutive integers > k, that generalizes Bertrand's postulate.
• Sylvester's law of inertia a.k.a. Sylvester's rigidity theorem, about the signature of a quadratic form.
• Sylvester's identity about determinants of submatrices.[5]
• Sylvester's criterion, a characterization of positive-definite Hermitian matrices.
• Sylvester domain.
• The Sylvester matrix for two polynomials.
• Sylvester's sequence, where each term is the product of previous terms plus one.
• Sylvester cyclotomic numbers.
• The Sylvester equation, AX + XB = C where A, B, C are given matrices and X is an unknown matrix.
• Sylvester's "four point problem" of geometric probability.
• The Sylvester expansion or Fibonacci–Sylvester expansion of a rational number, a representation as a sum of unit fractions found by a greedy algorithm.
• Sylvester’s rank inequality rank(A) + rank(B) − n ≤ rank(AB) on the rank of the product of an m × n matrix A and an n × p matrix B.
• Sylver coinage, a number-theoretic game.[6]

Other things named after Sylvester

• Sylvester (crater), an impact crater on the moon
• Sylvester Medal, given by the Royal Society for the encouragement of mathematical research[7]
• Sylvester (javascript library), a vector, matrix and geometry library for JavaScript

See also

• Sylvester's closed solution for the Frobenius coin problem when there are only two coins.
• Sylvester's construction for an arbitrarily large Hadamard matrix.
• Scientific equations named after people

References

1. Franklin, Fabian (1897), "James Joseph Sylvester", Bulletin of the American Mathematical Society, 3 (9): 299–309, doi:10.1090/S0002-9904-1897-00424-4, MR 1557527.
2. MathSciNet lists over 500 mathematics articles with "Sylvester" in their titles, most of which concern mathematical subjects named after Sylvester.
3. Borwein, P.; Moser, W. O. J. (1990), "A survey of Sylvester's problem and its generalizations", Aequationes Mathematicae, 40 (1): 111–135, CiteSeerX 10.1.1.218.8616, doi:10.1007/BF02112289.
4. Murty, U. S. R. (1969), "Sylvester matroids", Recent Progress in Combinatorics (Proc. Third Waterloo Conf. on Combinatorics, 1968), New York: Academic Press, pp. 283–286, MR 0255432.
5. Erwin H. Bareiss (1968), Sylvester's Identity and Multistep Integer- Preserving Gaussian Elimination. Mathematics of Computation, Vol. 22, No. 103, pp. 565–578
6. Berlekamp, Elwyn R.; Conway, John H.; Guy, Richard K. (1982), "Sylver Coinage", Winning Ways for your Mathematical Plays, Vol. 2: Games in Particular, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], pp. 576, 606, MR 0654502.
7. Cantor, Geoffrey (2004), "Creating the Royal Society's Sylvester Medal" (PDF), British Journal for the History of Science, 37 (1(132)): 75–92, doi:10.1017/S0007087403005132, MR 2128208